Make an object disappear by moving through a mesh
You could use a Boolean modifier:


Create a cube. It will be the object that will make your car disappear.
In the Properties panel > Object > Display, choose Maximum Draw Type > Wire. In the Properties panel > Object > Cycles Settings > Ray Visibility, disable everything. Your cube is now transparent in both Object and Render mode.
Select your car, give it a Boolean modifier, choose Operation > Difference, and choose the cube as the Object.
Now when you move your car, the part that touches the cube becomes invisible.